Koç University Graduate School of Business
MBA Program
OPSM 501: Operations Management
Week 11:
The Newsvendor Problem-ways to
avoid mismatch
Zeynep Aksin
zaksin@ku.edu.tr
Hammer 3/2 timeline and economics
Generate forecast
of demand and
submit an order
to TEC
Spring selling season
Nov Dec Jan
Feb Mar Apr May Jun
Receive order
from TEC at the
end of the
month
Jul Aug
Economics:
•
Each suit sells for
p = $180
•
TEC charges
c = $110 per suit
•
Discounted suits
sell for v = $90
Left over
units are
discounted

The “too much/too little problem”:
– Order too much and inventory is left over at the end of the season
– Order too little and sales are lost.

Marketing’s forecast for sales is 3200 units.
The demand-supply mismatch cost

Definition – the demand supply mismatch cost includes the cost of left over
inventory (the “too much” cost) plus the opportunity cost of lost sales (the
“too little” cost):
Mismatch cost  Co  Expected left over inventory
 Cu  Expected lost sales 

The maximum profit is the profit without any mismatch costs, i.e., every unit
is sold and there are no lost sales:
Maximum profit   p  c 

The mismatch cost can also be evaluated with
Mismatch cost = Maximum profit – Expected profit
Revisit Example 3:
Manufacturing cost=60TL,
Selling price=80TL, Discounted price (at the end of the season)=50TL
Market research gave the following probability distribution for demand.
Find the optimal q, expected number of units sold for this orders size, and
expected profit, for this order size.
Demand
500
600
700
800
900
1000
1100
Probability
0.10
0.2
0.2
0.2
0.10
0.10
0.10
P(D<=n-1)
0
0.1
0.3
0.5
0.7
0.8
0.9
Cu=20 Co=10
P(D<=n-1)<=20/30=0.66
<=0.66 q=800
For q=800:
E(units sold)=710
E(profit)=13,300
Max
profit=20*770=15400
When is the mismatch cost high?

Hammer 3/2’s mismatch cost as a percentage of the maximum profit is
$31,680/$223,440 = 14.2%

Mismatch cost as a percent of the maximum profit increases as …
– (1) the coefficient of variability of demand increases
– (2) the critical ratio decreases
Critical ratio
Coefficient
of variation
0.10
0.25
0.40
0.55
0.70
0.85
1.00
0.4
10%
24%
39%
53%
68%
82%
97%
0.5
8%
20%
32%
44%
56%
68%
80%
0.6
6%
16%
26%
35%
45%
55%
64%
0.7
5%
12%
20%
27%
35%
42%
50%
0.8
3%
9%
14%
19%
24%
30%
35%
0.9
2%
5%
8%
11%
14%
17%
19%
Options to reduce the mismatch cost
 Make to order
 Reactive Capacity
– Unlimited
– Limited
Make-to-Stock Model
Suppliers
Assembly
Configuration
7
Assemble-to-Order Model
Suppliers
Assembly
Configuration
8
Unlimited, but expensive reactive capacity
 TEC charges a premium of 20% per unit ($132 vs. $110) in the
second order.
 There are no restrictions imposed on the 2nd order quantity.
 O’Neill forecast of total season sales is nearly perfect after
observing initial season sales.
 How many units should O’Neill order in October?
12-9
Revisit Example 2: Finding Cu and Co
A textile company in UK orders coats from China. They buy a coat from
250€ and sell for 325€. If they cannot sell a coat in winter, they sell it
at a discount price of 225€. When the demand is more than what
they have in stock, they have an option of having emergency
delivery of coats from Ireland, at a price of 290.
The demand for winter has a normal distribution with mean 32,500
and std dev 6750.

How much should they order from China??
Example 2: Finding Cu and Co
A textile company in UK orders coats from China. They buy a coat from
250€ and sell for 325€. If they cannot sell a coat in winter, they sell it at
a discount price of 225€. When the demand is more than what they
have in stock, they have an option of having emergency delivery of
coats from Ireland, at a price of 290.
The demand for winter has a normal distribution with mean 32,500 and
std dev 6750.

How much should they order from China??
Cu=75-35=40
Co=25
F(z)=40/(40+25)=40/65=0.61z=0.28
 q=32500+0.28*6750=34390
Apply Newsvendor logic even with a 2nd
order option

The “too much cost” remains the same:
– Co = c – v = 110 – 90 =20.

The “too little cost” changes:
– If the 1st order is too low, we cover the difference with the 2nd order.
– Hence, the 2nd order option prevents lost sales.
– So the cost of ordering too little per unit is no longer the gross margin, it
is the premium we pay for units in the 2nd order.
• Cu = 132 – 110 = 22
Cu
22

 0.5238
Co  Cu 20  22

Critical ratio:

Corresponding z-statistic F(0.05)=0.5199, F(0.06)=0.5239, so z = 0.06.
Q    z  3192  0.06  1181  3263
Profit improvement due to the 2nd order
option

With a single ordering opportunity:
– Optimal order quantity = 4101 units
– Expected profit = $191,760
– Mismatch cost as % of revenue = 4.9%

The maximum profit is unchanged = $223,440

With a second order option:
– Optimal order quantity = 3263 units
Expected profit  Maximum profit - Co  Expected left over inventory
 Cu  Expected second replenishm ent quantity 
 $223,440  $20  508  $22  437 
 $203,666
– Reduction in mismatch cost = 38% (19,774 vs 31,680)
– Mismatch cost as % of revenue = 3.1%
Limited reactive capacity
 Units in the 2nd order are no more expensive
than in the 1st order
 But there is limited capacity for a 2nd order
Sport
Sample of wetsuits
Model
DIVE
DIVE COMP 3/2 FULL
DIVE
WMS 7000X 7MM FULL
SURF
EPIC 5/3 W/HD
SURF
HEAT 3/2
SURF
HEATWAVE 4/3
SURF
ZEN-ZIP 4/3
TRIATHLON
TRIATHLON 4/3 FULL
WAKE-BOARD REACTOR 3/2
WINDSURF
CYCLONE 4/3
WINDSURF
WMS EVOLUTION 4/3
 = expected demand



1100 660
600 360
800 296
1200 444
700 259
3100 1147
2600 1690
1500 750
950 665
850 595
0.60
0.60
0.37
0.37
0.37
0.37
0.65
0.50
0.70
0.70
Price Margin Discount
120
275
225
110
140
165
210
150
325
275
38%
38%
38%
38%
38%
38%
45%
45%
45%
45%
65%
65%
50%
50%
50%
50%
65%
65%
65%
65%
 = standard deviation of demand
Price = wholesale price
Margin = gross margin as a % of price
Discount = anticipated end of season discount as % of price to sell left over inventory
 1st order must be at least 10,200 suits so that there is
enough capacity for the 2nd order.
 Also a minimum order quantity-order once
 What should we produce in the 1st order?
Profit and mismatch with only 1 ordering
opportunity

Use the Newsvendor model to evaluate the optimal order quantity, expected
profit, maximum profit and mismatch cost
Sport
DIVE
DIVE
SURF
SURF
SURF
SURF
TRIATHLON
WAKE BOARD
WINDSURF
WINDSURF
Total
Model
DIVE COMP 3/2 FULL
WMS 7000X 7MM FULL
EPIC 5/3 W/HD
HEAT 3/2
HEATWAVE 4/3
ZEN-ZIP 4/3
TRIATHLON 4/3 FULL
REACTOR 3/2
CYCLONE 4/3
WMS EVOLUTION 4/3
Order
quantity
1241
677
1009
1514
883
3910
3449
1877
1284
1149
16993
Expected
Maximum Mismatch
profit
profit
cost
$30,086
$50,160 $20,074
$37,608
$62,700 $25,092
$58,048
$68,400 $10,352
$42,568
$50,160
$7,592
$31,604
$37,240
$5,636
$164,953
$194,370 $29,417
$164,582
$245,700 $81,118
$75,536
$101,250 $25,714
$89,538
$138,938 $49,399
$67,788
$105,188 $37,399
$762,311 $1,054,105 $291,794
12-16
Produce “safer” products early, produce
“risky” products with reactive capacity


Sort items by their mismatch cost to order quantity ratio.
Fill the 1st order up to the minimum quantity (10,200) with the items that
have the lowest mismatch – quantity ratio
Order
quantity
Model
HEAT 3/2
1514
HEATWAVE 4/3
883
ZEN-ZIP 4/3
3910
EPIC 5/3 W/HD
1009
REACTOR 3/2
1877
DIVE COMP 3/2 FULL
1241
TRIATHLON 4/3 FULL
3449
WMS EVOLUTION 4/3
1149
WMS 7000X 7MM FULL
677
CYCLONE 4/3
1284
Total
16993
Newsvendor
expected Mismatch
profit
cost
$42,568
$7,592
$31,604
$5,636
$164,953 $29,417
$58,048 $10,352
$75,536 $25,714
$30,086 $20,074
$164,582 $81,118
$67,788 $37,399
$37,608 $25,092
$89,538 $49,399
$762,311 $291,794
Mismatch costorder quantity First order
ratio
quantity
Profit
5.0
1514 $42,568
6.4
883 $31,604
7.5
3910 $164,953
10.3
1009 $58,048
13.7
1877 $75,536
16.2
1241 $30,086
23.5
0 $245,700
32.6
0 $105,188
37.1
0 $62,700
38.5
0 $138,938
10434 $955,320
12-17
Push-Pull Supply Chains
The Supply Chain Time Line
Customers
Suppliers
PUSH STRATEGY
Low Uncertainty
PULL STRATEGY
High Uncertainty
Push-Pull Boundary
18
A new Supply Chain Paradigm
 A shift from a Push System...
– Production decisions are based on forecast
 …to a Push-Pull System
– Parts inventory is replenished based on forecasts
– Assembly is based on accurate customer demand
19
Demand Forecast
 The three principles of all forecasting techniques:
– Forecasts are always wrong
– The longer the forecast horizon the worst is the
forecast
– Aggregate forecasts are more accurate
• The Risk Pooling Concept
20
Business models in the Book Industry
 From Push Systems...
– Barnes and Noble
 ...To Pull Systems
– Amazon.com, 1996-1999
 And, finally to Push-Pull Systems
– Amazon.com, 1999-present
• Around 40 warehouses
21
Business models in the Grocery Industry
 From Push Systems...
– Supermarket supply chain
 ...To Pull Systems
– Peapod, 1989-1999
• Stock outs 8% to 10%
 And, finally to Push-Pull Systems
– Peapod, 1999-present
• Dedicated warehouses
• Stock outs less than 2%
22
Locating the Push-Pull Boundary
23
Organizational Skills Needed
Raw
Material
Customers
Push
Pull
Low Uncertainty
High Uncertainty
Long Lead Times
Short Cycle Times
Cost Minimization
Service Level
Resource Allocation
Responsiveness
24
O’Neill: quick response (reactive capacity)
Low Risk: Push
Speculative
Production capacity
Initial forecast
High Risk: Push-Pull
Reactive
Production capacity
Later orders
25
Announcement
 Read the HP case for next week
 We will analyze it in-class
 Bring your laptops!